A number‐between‐events control chart for monitoring finite horizon production processes

Abstract

In this paper, we present a number‐between‐events (NBE) control chart for monitoring the fraction nonconforming in finite horizon production (FHP) processes and related specific performance measures. When monitoring fractions nonconforming in FHP processes, the common binomial p$p$‐chart has two crucial limitations: the underlying distributional assumptions are violated when dealing with low‐volume production and a scarce efficiency in the case of processes characterized by a low fraction nonconforming. Thus, an efficient monitoring of FHP processes requires the selection of the correct underlying statistical model: in this case, a distribution from the hypergeometric family of discrete statistical distributions. An efficient statistical monitoring of processes with low fractions nonconforming can be achieved by means of discrete time‐between‐events (TBE) control charts, which count the number of units up to the appearance of a fixed number of nonconforming units in the sample. Here, we present a discrete TBE‐chart, denoted as NBE‐chart, based on the negative hypergeometric distribution that meets numerous requirements of efficient monitoring of FHP processes. The proposed control chart can be conveniently used for both low‐volume and mass production in processes with frequent changeovers.

Symmetrical and Asymmetrical Distributions in Statistics and Data Science

“…We would therefore like to invite researchers to submit their contributions to Volume II of this Special Issue. A potential topic of interest could be the remarkable revival of the hypergeometric and the negative hypergeometric distribution in various areas such as healthcare [14], manufacturing [15], risk management [16], statistical inference [17], and beyond. We look forward to many high-quality papers and a successful second edition of this Special Issue.…”